Despite football's collaborative nature, the inquiry into the identity of the best player is a frequent topic in the footballing realm. This discussion disproportionately highlights attacking players, creating an apparent bias, as every team role holds significance. Our study aimed to delineate player performance from team performance and ensure the inclusion of players from all positions in the ultimate ranking of the best players. We sourced data from FBref, encompassing every player in every match played by a top 20 European team in the current century's top 5 European leagues. Employing a multilevel linear mixed-efects model, we utilized team points as the response variable, accounting for both player and opponent team strength. The extraction of level-2 player residuals, averaged by player, facilitated the creation of a comprehensive ranking for the best players of this century. Surprisingly, two players widely regarded as among the best of all time, Messi and Ronaldo, secured relatively low positions on our list (Ronaldo at 12th, and Messi at 14th).
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Despite football being a team sport, determining the best male football player remains a widely debated topic. In every era, a standout candidate emerges—Pelé in the 1960s, Diego Maradona in the 1980s, and more recently, Lionel Messi and Cristiano Ronaldo dominating the past 15 years. The ongoing debate centers on which of these four players is the all-time best. Our attempt to provide a data-driven solution was hindered by the historical match data’s poor quality, leading CEUR Workshop Proceedings the best player debate. Goals scored, being the most coveted statistic, contributes to this bias. Defenders’ performance is typically measured by goals conceded per game, yet this metric is assigned to the entire defense, creating an imbalance in player position evaluation. Our second research objective aimed to rectify this bias and provide a fair comparison among players irrespective of their position or style of play.
To fulfill our research goals—ranking players based on impact and ensuring equal opportunities for all positions—we employed a multilevel mixed-efects model. This model, utilizing achieved points in the game as a performance metric, underwent training on the last 23 seasons of every league match involving the top 20 European football teams across the top 5 European leagues.
In this section, we explore prior research on ranking individual ability and multilevel modeling in team sports.
Brooks et al. [
Pappalardo et al. [
Mixed-efects modeling in football research includes Grund [
Inspired by Bell et al. [
The linear mixed-efects model, also referred to as a mixed model, random efects model,
multilevel model, or hierarchical model, serves as a statistical model tailored for hierarchical
data [
This model empowers the control of variables at higher levels, efectively addressing the variation and correlation within the data structure to yield more precise outcomes. It encompasses ifxed variables, representing coeficients with a consistent impact on the response variable across all groups, and at least one random variable, introducing a variable efect contingent on the group.
Building upon a fundamental linear regression model, the mixed-efects model enables the
variation of intercepts and/or slopes of the regression line across diferent data groups for select
variables. For instance, in a study by Bell et al. [
Consider predicting students’ performance on the fictional National Test of Mathematics based on their average percentage of points achieved in their Mathematics class. The data is nested on two levels: the school (School A and School B) and the student. Each data point represents a student’s average percentage in class and the competition.
School A is known for its strict grading, while School B is more lenient. Predicting overall performance without accounting for school variations would be inaccurate due to the substantial diference in expected competition scores between the schools.
The mixed-efects multilevel model addresses this issue by allowing control for school, enhancing prediction accuracy. In our case, random slopes are not suitable; thus, random intercepts and fixed percentages of points in school are included in the formula: = ( 0 + 0,ℎ ) + ( 1 + 1,ℎ ) ⋅ ℎ + Here, 0 and 1 represent the overall intercept and slope, 0,ℎ and 1,ℎ variations by school, and is the student’s residual. The overall regression line is: account for = ℎ − 5.3 The school-specific lines are: = 0.81 ⋅ ℎ + 24.5 = 1.18 ⋅ ℎ − 35.1 (School A) (School B)
Intercept and slope values for the overall and school-specific cases are presented in Table ??.
In our study, we employed a similar framework featuring two fixed efects (opponents’s points per game and home or away indicator) and 3 random efects (team, team in a particular season, and player). These incorporate random intercepts and slopes, varying based on the predicting variables. The data is nested across four levels, comprising 20 teams, each spanning multiple seasons, players associated with one or multiple clubs across diferent seasons, and repeated measures for every match of every player.
For instance, Cristiano Ronaldo participated in 597 matches over 14 seasons for 3 diferent clubs. Teams varied in participation, with RB Leipzig, for instance, joining the Bundesliga from the 18/19 season onwards but achieving significant success in those four seasons, securing a spot in our top 20 teams list.
To identify the best football player, we established criteria defining a standout player as someone who consistently elevated top teams in the premier European leagues—English, Spanish, Italian, German, and French divisions—over an extended period.
Data from the top five European leagues was scraped from FBref [
We filtered players with a minimum of 340 matches for the top 20 teams across the leagues, setting the threshold close to a full season. Additionally, players with fewer than 15 minutes of playtime were excluded, ensuring impactful player contributions.
For the multilevel mixed-efects model, we utilized the ”lmer” function from lme4 [13] in R.
Model building, inspired by Bell et al. [
Player-specific intercepts and slopes were obtained using the ”ranef” function from lme4 [13]. A custom function calculated player contributions to matches, extracting level-2 residuals. Team residuals were similarly extracted for the top 20 list.
In Table 1, the ranking displays players with over 340 league games for the top 20 teams in the top 5 European leagues. Players are ordered by mean residual values, showcasing their impact on team performance. Giorgio Chiellini leads the ranking with a mean value of 4.091820 × 10−9, signifying an average improvement in his team’s performance when he played—he contributed to scoring more points. Conversely, Marcelo had a negative impact on his team, indicated by a mean value of −4.280433 × 10−9. In simpler terms, when Giorgio Chiellini played, he, on average, exceeded predicted team performance by 4.091820 × 10−9 points.
Football, despite being a team sport, perpetually raises the question of the best player, creating endless debates and discussions. Opinions, often subjective, vary based on personal criteria. Notably, ofensive players dominate discussions, overshadowing the defensive aspect, crucial but overlooked. This study aims to objectively extract player performances from team data, ofering an equitable assessment of all roles.
Our definition of a good player hinges on their team’s reliance—a player missed when absent, impacting team performance. To ensure an accurate evaluation, we employed a multilevel mixed-efects model, controlling for team strength. Data from FBref encompassed player and team details, match points, home/away status, season, and opposition’s average points per game. A linear mixed-efects model allowed us to control for team strength, with extracted level-2 player residuals forming the final rankings.
The list featured impactful players in this century, with Giorgio Chiellini topping, followed by Andrea Pirlo and Petr Čech. Surprisingly, iconic players like Ronaldo and Messi ranked 12th and 14th. The top 30 showed balance across positions—8 goalkeepers, defenders, and midfielders, and 6 attackers.
Player level-2 residuals were small due to players’ extensive playing time, emphasizing team and team season efects. Future exploration could widen the timeframe, create leaguespecific rankings, and incorporate diverse metrics for player contribution, potentially examining managerial impact and expanding related studies to extensive periods.
This work has received support from the research program CogniCom (0013103) at the University of Primorska. [11] K. Reitz, requests: Python HTTP for Humans., 2023. URL: https://requests.readthedocs.io. [12] Crummy, Beautiful Soup 4.12.0 documentation, 2023. URL: https://www.crummy.com/ software/BeautifulSoup/bs4/doc/. [13] lme4, lme4 package, 2023. URL: https://github.com/lme4/lme4.